The amount of money that Maria earns in a week is a random variable with a mean of $970 and a standard deviation of $25.The amount of money that Elena earns in a week is a random variable with a mean of $860 and a standard deviation of $10.How much more do you expect Maria to earn in a week than Elena? What is the standard deviation of this difference? Assume that Maria's earnings are independent of Elena's earnings.

A) $1830,$35
B) $110,$26.93
C) $110,$22.91
D) $110,$15
E) $1830,$26.93

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danielle wickman · Accepted Answer

Final Answer : B, Explanation :   The difference in earnings, $D$, is given by: D = Maria’s earnings  −  Elena’s earnings D = 	ext{Maria ' s earnings } - 	ext{ Elena ' s earnings} D = Maria’s earnings  −  Elena’s earnings The mean of $D$ is: E ( D ) = E ( Maria’s earnings ) − E (  Elena’s earnings ) = $ 970 − $ 860 = $ 110 E(D) = E(	ext{Maria ' s earnings}) - E(	ext{ Elena ' s earnings}) = \$970 - \$860 = \$110 E ( D ) = E ( Maria’s earnings ) − E (  Elena’s earnings ) = $970 − $860 = $110 The standard deviation of $D$ is: Var ( D ) = Var ( Maria’s earnings ) + Var (  Elena’s earnings ) = 2 5 2 + 1 0 2 = 675 	ext{Var}(D) = 	ext{Var}(	ext{Maria ' s earnings}) + 	ext{Var}(	ext{ Elena ' s earnings}) = 25^2 + 10^2 = 675 Var ( D ) = Var ( Maria’s earnings ) + Var (  Elena’s earnings ) = 2 5 2 + 1 0 2 = 675 So, the standard deviation of $D$ is: SD ( D ) = Var ( D ) ≈ $ 26.93 	ext{SD}(D) = \sqrt{	ext{Var}(D)} \approx \$26.93 SD ( D ) = Var ( D ) ​ ≈ $26.93 Therefore, we can expect Maria to earn about \$110 more than Elena, with a standard deviation of \$26.93.

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